Compare the functions f(x)=x3+1 and g(x)=x+1. Which of the following statements is true about the intercepts of the functions?
The function f(x)=x^3+1 is a cubic function, while the function g(x)=x+1 is a linear function.
To find the x-intercept of a function, we set y to zero and solve for x. For f(x), we have:
0 = x^3 + 1
By subtracting 1 from both sides, we get:
x^3 = -1
Taking the cubic root of both sides, we have:
x = -1
Therefore, the x-intercept of f(x) is -1.
To find the y-intercept of a function, we set x to zero and solve for y. For g(x), we have:
y = 0 + 1
So the y-intercept of g(x) is 1.
In summary:
- The x-intercept of f(x) is -1.
- The y-intercept of g(x) is 1.
Therefore, the statement "The x-intercept of f(x) equals the y-intercept of g(x)" is true.